In 1999, The US AIr Force Academy Studied Cookies. No, Not The Internet Kind.

The United States Air Force Academy, in response to the “Chips Ahoy! 1,000 Chips Challenge”, calculated that there were a total of 52,986 chocolate chips in 42 18-ounce bags of Chips Ahoy! cookies. The sample mean is 1261.6 and the sample standard deviation is 117.6.

Each 18-ounce bag of cookies contains 48 individual cookies. If a single cookie is picked at random, which of the following numbers of chocolate chips is it most likely to have:

23 25 29 27

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8 solutions

Krisada Muangsri
Jan 15, 2014

There are 1261.6 chips/bag Each bag has 42 pieces of cookies so, there are about 1261.6/42 = 26.28 => 27 chips/cookies

i agree the sol. you cannot round off 26.28 cookies to 26, that 0.28 part is obtained from the 27th cookie, so therefore there are 27 cookies,

Noel Maglasang - 7 years, 4 months ago

i did the same

Rohitas Bansal - 7 years, 4 months ago

26.283 is near to 26 rather than 27 . then how 27 ??

Aakhilsehabaz Shaik - 7 years, 4 months ago

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Sometimes you have to look in the options too.. :P

Manoj Majumdar - 7 years, 4 months ago
Regalado Inigo
Jan 13, 2014

1261.6 divided by 42 will get you around 30 (the mean number of chips in a random cookie)

117.6 divided by 42 will get you 2.8, round off to 3 (Standard deviation)

so the answer should be...

30 +/- 3...... either 27 or 33

you have to divide by 48. You will get 26.2 +/- 2.5, which is closest to 27.

Ronald Overwater - 7 years, 5 months ago

Total chip spread over the cookies equally in every bag : 52,986/42/48 = 26.2 (say 27).

Agung Budiarto - 7 years, 4 months ago

But there were 48 cookies per bag so the range of possible amounts of chips were 29-23. I thus chose 25 because it was closer to 26 which would be the mean of that range of numbers which answer wasn't a possible answer, but 27 is equally close to 26 which would be the answer if it were a possible choice. So it could be 25 or 27.

Rose Huntress-Ristich - 7 years, 2 months ago

The mean number of chocolate chips in the sample is 1261.6 per bag. Since there are 48 cookies per bag, the mean number of chocolate chips per cookie is: 1261.6 48 = 26.283 \frac{1261.6}{48}=26.283

The possible choice closest to this answer is 27 \boxed{27} .

26.283 is near to 26 not 27 ? ??

Aakhilsehabaz Shaik - 7 years, 4 months ago

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26 is not one of the choices.

A Former Brilliant Member - 7 years, 4 months ago
Ks Sk
Jan 16, 2014

There are multiple distractions in this question. There is a sample size, and standard deviation. Don't go calculating standard errors (SE) here. Not necessary yet. The question is simply: If a cookie is chosen, how many chocolate chips will it have on an average?

The question actually boils down to 3 steps:

a) The number of cookies in the bag -- 48

b) The number of chocolate chips in a bag of Chips ahoy -- 1261.6

Hence, <b> average number of chips per cookie = 1261.6/48 = 26.28 </b>

c) You don't see this exact answer (how can you have .28 of a chip? :)) but since the question asks "most likely", you know you need to find the closest number to 26.28, i.e. 27

Well, this is a correct solution

Akshay Gupta - 7 years, 4 months ago
Kajal Jain
Feb 27, 2014

27

Tauassul Rashique
Feb 20, 2014

27

Shuva Dev
Feb 5, 2014

27

Rashid Adeel
Jan 21, 2014

I guess

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